Capacitance type acceleration sensor

ABSTRACT

A capacitance type acceleration sensor includes a semiconductor substrate, a weight portion supported with the substrate through a spring portion, a movable electrode integrated with the weight portion, and a fixed electrode cantilevered with the substrate. The movable electrode is displaced along with a facing surface of the movable electrode in accordance with acceleration. The facing surface of the movable electrode faces a facing surface of the fixed electrode so as to provide a capacitor. The capacitance of the capacitor changes in accordance with a displacement of the movable electrode so that an outer circuit detects the acceleration as a capacitance change. Each facing surface of the movable and fixed electrodes has a concavity and convexity portion for increasing the capacitance change.

CROSS REFERENCE TO RELATED APPLICATION

This application is based on Japanese Patent Application No. 2002-336802filed on Nov. 20, 2002, the disclosure of which is incorporated hereinby reference.

FIELD OF THE INVENTION

The present invention relates to a capacitance type acceleration sensorhaving high sensitivity.

BACKGROUND OF THE INVENTION

A capacitance type acceleration sensor according to a prior art isdisclosed in U.S. Pat. No. 6,151,966. The sensor includes a movableelectrode and a fixed electrode, each of which has a plurality of teeth.The movable electrode faces the fixed electrode so that they form acapacitor. When acceleration is applied to the sensor, a movable portionhaving a weight portion and the movable electrode in the sensor isdisplaced. Then, the capacitance of the capacitor changes in accordancewith the displacement of the movable electrode. This capacitance changeis measured so that the acceleration is detected. Here, the movableelectrode is integrated with the weight portion, and the displacementdirection of the movable electrode is perpendicular to a facing surfaceof the movable electrode. The facing surface of the movable electrodefaces the fixed electrode. When the movable electrode moves toward thefixed electrode and the distance between the movable and fixedelectrodes becomes small, the capacitance becomes larger. When thedistance between the movable and fixed electrodes becomes large, thecapacitance becomes smaller.

When the movable electrode is displaced, a squeeze damping effect isgenerated by viscosity of air disposed between the movable electrode andthe fixed electrode. Particularly, the squeeze damping works between thefacing surfaces of the movable and fixed electrodes. Therefore, when thesensor detects the acceleration near a resonant frequency of the movableportion, the displacement of the movable electrode and the capacitancechange in accordance with the displacement become small, so that fineacceleration may not be detected. Namely, the sensor sensitivity isdecreased.

SUMMARY OF THE INVENTION

In view of the above problem, it is an object of the present inventionto provide a capacitance type acceleration sensor having highsensitivity.

A capacitance type acceleration sensor includes a semiconductorsubstrate, a weight portion supported with the substrate through aspring portion, a movable electrode integrated with the weight portion,and a fixed electrode cantilevered with the substrate. The movableelectrode together with the weight portion is displaced along with afacing surface of the movable electrode in accordance with accelerationapplied to the weight portion. The facing surface of the movableelectrode faces a facing surface of the fixed electrode so as to providea capacitor having a capacitance. The capacitance of the capacitorchanges in accordance with a displacement of the movable electrode sothat an outer circuit detects the acceleration as a capacitance change.Each facing surface of the movable and fixed electrodes has a concavityand convexity portion for increasing the capacitance change.

In the above sensor, the capacitance change becomes larger because ofthe concavity and convexity portion. Therefore, the sensor sensitivityis improved so that the sensor has high sensitivity.

Preferably, each of the movable and fixed electrodes has a plurality ofteeth, and the teeth of the movable and fixed electrodes are disposedalternately so that sidewalls of the teeth provide the facing surfaces.Further, the movable electrode has a predetermined shape in such amanner that the movable portion resonates at a vibration frequency ofthe acceleration for increasing the capacitance change. In this sensor,the movable portion is formed to resonate at the acceleration vibrationfrequency, and the movable portion is displaced along with the facingsurface, in which the movable portion is affected with the slide dampingeffect. Accordingly, the magnification of resonance becomes larger, sothat the displacement of the movable portion becomes large. Thus, thecapacitance change is also increased, so that the sensor sensitivity isimproved.

Preferably, each concavity and convexity portion of the movable andfixed electrodes has a plurality of convexities and concavities, andeach convexity of the movable electrode faces the convexity of the fixedelectrode, respectively, when no acceleration is applied. Morepreferably, each of the convexities and the concavities has a length ina displacement direction of the movable electrode, and the length of theconvexity is equal to or longer than that of the concavity. Morepreferably, the length of the concavity is equal to or larger than twiceof a maximum displacement of the movable portion. In this case, therelationship between the capacitance change and the displacement of themovable portion monotonically increases or decreases, so that the sensorcan detect the acceleration easily.

Preferably, part of the convexity of the movable electrode faces theconvexity of the fixed electrode when no acceleration is applied. Inthis case, the sensor can detect the direction of the acceleration bydetecting the increase and decrease from the initial capacitance.

Further, a capacitance type acceleration sensor includes a semiconductorsubstrate, a weight portion supported with the substrate through aspring portion, a movable electrode integrated with the weight portion,and a fixed electrode cantilevered with the substrate. The movableelectrode together with the weight portion is displaced perpendicularlyto a facing surface of the movable electrode in accordance withacceleration applied to the weight portion. The facing surface of themovable electrode faces a facing surface of the fixed electrode so as toprovide a capacitor having a capacitance. The capacitance of thecapacitor changes in accordance with a displacement of the movableelectrode so that an outer circuit detects the acceleration as acapacitance change. The movable electrode protrudes from both sidewallsof the weight portion, the sidewall being perpendicular to thesubstrate. Each of the movable electrode and the weight portion has aheight in a perpendicular direction perpendicular to the substrate. Theheight of the movable electrode is substantially equal to that of theweight portion. Each facing surface of the movable and fixed electrodeshas a length in a protrusion direction of the movable electrode and aheight in the perpendicular direction of the substrate. The length ofthe facing surface is equal to or smaller than the height of the facingsurface.

In the above sensor, the capacitance change becomes larger so that thesensor sensitivity is improved and the sensor has high sensitivity.

Preferably, each of the movable and fixed electrodes has a plurality ofteeth, and the teeth of the movable and fixed electrodes are disposedalternately so that sidewalls of the teeth provide the facing surfaces.Further, the movable electrode has a predetermined shape in such amanner that the movable portion resonates at a vibration frequency ofthe acceleration for increasing the capacitance change. In this case,the magnification of resonance is increased, and the displacement of themovable portion at the resonance point is also enhanced, so that thecapacitance change becomes large. Thus, the sensor sensitivity isimproved so that the sensor can detect a fine acceleration.

Furthermore, a capacitance type acceleration sensor includes asemiconductor substrate, a weight portion supported with the substratethrough a spring portion, a movable electrode integrated with the weightportion, and a fixed electrode cantilevered with the substrate. Themovable electrode together with the weight portion is displaced towardthe fixed electrode in accordance with acceleration applied to theweight portion. The movable electrode includes a facing surface facing afacing surface of the fixed electrode so as to provide a capacitorhaving a capacitance. The capacitance of the capacitor changes inaccordance with a displacement of the movable electrode so that an outercircuit detects the acceleration as a capacitance change. Each facingsurface of the movable and fixed electrodes inclines at a predeterminedangle with respect to a displacement direction. The predetermined angleis in a range between 0° and 90°.

In the above sensor, the capacitance change becomes larger so that thesensor sensitivity is improved and the sensor has high sensitivity.

Preferably, each of the movable and fixed electrodes has a plurality ofteeth, and the teeth of the movable and fixed electrodes are disposedalternately so that sidewalls of the teeth provide the facing surfaces.Further, the movable electrode has a predetermined shape in such amanner that the movable portion resonates at a vibration frequency ofthe acceleration for increasing the capacitance change. In this case,the capacitance change becomes much larger, so that the sensor candetect a fine acceleration.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other objects, features and advantages of the presentinvention will become more apparent from the following detaileddescription made with reference to the accompanying drawings. In thedrawings:

FIG. 1 is a schematic perspective view showing a pair of facing surfacesof fixed and movable electrodes in a capacitance type accelerationsensor according to a first embodiment of the present invention;

FIG. 2 is a graph showing a relationship between amplitude δ andfrequency ratio ω/ωn in the sensor according to the first embodiment;

FIG. 3A is a schematic plan view showing a sensing portion of thesensor, FIG. 3B is a cross-sectional view showing the sensing portiontaken along line IIIB-IIIB in FIG. 3A, and FIG. 3C is an enlarged planview showing part of the sensing portion of IIIC in FIG. 3A, accordingto the first embodiment;

FIGS. 4A to 4D are cross-sectional views of the sensor explaining amanufacturing method of the sensor according to the first embodiment;

FIGS. 5A to 5C are enlarged plan view showing part of the sensingportion of IIIC in FIG. 3A for explaining an arrangement of the movableand fixed electrodes;

FIGS. 6A to 6C are schematic perspective views showing a pair of facingsurfaces of the fixed and movable electrodes in a capacitance typeacceleration sensor according to a second embodiment of the presentinvention;

FIG. 7 is a graph showing a relationship between aspect ratio L/H anddamping coefficient E or capacitance change ΔCo in the sensor accordingto the second embodiment;

FIG. 8 is a perspective view showing the sensor according to the secondembodiment;

FIGS. 9A to 9F are schematic perspective views showing a pair of facingsurfaces of the fixed and movable electrodes in a capacitance typeacceleration sensor according to a third embodiment of the presentinvention;

FIG. 10 is a plan view showing a sensing portion of the sensor accordingto the third embodiment;

FIGS. 11A to 11C are schematic perspective views showing the facingsurface in the different sensors according to the third embodiment; and

FIG. 12 is a graph showing a relationship between tilt angle θ andcapacitance change ΔCo in the different sensors according to the thirdembodiment.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS First Embodiment

With using resonant effect, a capacitance type acceleration sensoraccording to a first embodiment of the present invention detects fineacceleration, for example, under 1G (i.e., under the gravitationalconstant). The sensor is suitably used for a vibration sensor or agyroscope. The vibration sensor detects a bone conduction soundconducting through a bone.

Referring to FIGS. 1 and 2, function and operation of the sensor withusing the resonant effect will be explained as follows. The resonantfrequency of the sensor is set in a measurement frequency range so thata displacement of a movable portion in the sensor is amplified becauseof the resonant effect. In this case, damping effect of the movableportion relates to the amplification of the displacement.

As shown in FIG. 1, a movable electrode 1 and a fixed electrode 2 in thesensor have facing surfaces, respectively. Each facing surface of themovable and fixed electrodes 1, 2 faces each other. Damping effect worksbetween the facing surfaces of the movable and fixed electrodes 1, 2because of viscosity of air disposed between the facing surfaces. Whenthe movable electrode 1 is displaced in a perpendicular direction Pperpendicular to the facing surface, the squeeze damping effect isappeared. When the movable electrode is displaced along with the facingsurface, i.e., in a sliding direction S, a slide damping effect isappeared.

In a conventional capacitance type acceleration sensor, since thedistance between the movable and fixed electrodes is shorter than thelength of the facing surface, the movable electrode is movable in theperpendicular direction perpendicular to the facing surface so that apredetermined displacement makes much more capacitance change. However,in the conventional sensor, as the distance between the movable andfixed electrodes becomes shorter, it is difficult to detect fineacceleration because the squeeze damping effect appeared between theelectrodes becomes larger in accordance with the displacement of themovable electrode.

Consequently, in the sensor according to the first embodiment, themovable portion 1 is set to move in a sliding direction S (i.e., thedirection along with the facing surface), in which the damping effectbecomes small. Simultaneously, the displacement of the movable portion 1is amplified by the resonant effect. In this case, even when fineacceleration is applied to the sensor, the capacitance change becomeslarge so that the sensor can detect the fine acceleration.

The above method is explained with using numerical formulas.$\begin{matrix}{{\Delta\quad{Co}} = \frac{ɛ\quad{HX}}{D}} & ({F1}) \\{{{M\overset{¨}{X}} + {E\overset{.}{X}} + {KX}} = {F\quad{\cos( {\omega\quad T} )}}} & ({F2}) \\{X = {\frac{\delta\quad{st}}{\sqrt{( {1 - ( \frac{\omega}{\omega\quad n} )^{2}} )^{2} + ( {\frac{1}{Q}\frac{\omega}{\omega\quad n}} )^{2}}}{\cos( {{\omega\quad T} - \beta} )}}} & ({F3}) \\{Q = {\frac{\sqrt{MK}}{E} = {\frac{M}{E}\omega\quad n}}} & ({F4}) \\{{\delta\quad{st}} = {\frac{M}{K}\alpha}} & ({F5})\end{matrix}$

Here, ΔCo represents capacitance change, ε a dielectric constant, H aheight of the facing surface of a pair of the movable electrode and thefixed electrode, D a distance between the movable electrode and thefixed electrode, X a displacement of the movable electrode, M a mass ofa movable portion, E a damping coefficient of the movable portion, K aspring constant, F vibration force of amplitude, ω a frequency ofvibration, β a delay angle, an a resonant frequency of vibration, Q amagnification of resonance (i.e., a Q-value), δst a static amplitude,and a acceleration.

Formula F1 shows a relationship between the capacitance change ΔCocorresponding to the sensor sensitivity of the sensor and thedisplacement X of the movable electrode 1. The displacement X shows adisplacement in the sliding direction S along with the facing surface.Formula F2 shows a dynamic equation of the movable portion 1. Thesolution of the dynamic equation F2 is shown as Formula F3. Formula F4defines the magnification of resonance Q. Formula F5 shows arelationship between the acceleration α and the static amplitude δst.

Here, the maximum amplitude δ of the movable portion is obtained byFormula F6. $\begin{matrix}{\delta = \frac{\delta\quad{st}}{\sqrt{( {1 - ( \frac{\omega}{\omega\quad n} )^{2}} )^{2} + ( {\frac{1}{Q}\frac{\omega}{\omega\quad n}} )^{2}}}} & ({F6})\end{matrix}$

FIG. 2 also shows the relationship between the maximum amplitude δ andthe frequency ratio ω/ωn in case of various magnifications of resonanceQ at the resonant frequency on obtained by Formula F4. In a case wherethe frequency of vibration ω coincides with the resonant frequency ofvibration ωn, i.e., in case of resonance point (ω=ωn), Formula F6 isdisplaced as Formula F7.δ=Qδst  (F7)

Accordingly, at the resonance point, the amplitude δ, i.e., thedisplacement X shows Q-fold of the static amplitude δst. Here, themagnification of resonance Q and the damping coefficient E have therelationship of Formula F4. When the movable electrode 1 is displaced inthe sliding direction S along with the facing surface of the movableelectrode 1, the slide damping effect is appeared between the electrodes1, 2, so that the damping coefficient E becomes small. That is becausethe magnitude of the slide damping effect is smaller than that of thesqueeze damping effect. Therefore, the slide damping effect does notmuch affect the sensor 100, so that the magnification of resonance Qbecomes larger. Then, the displacement X shown in Formula F3 isincreased, and the capacitance change ΔCo becomes larger. Thus, thesensor sensitivity is improved.

The sensor 100 according to the first embodiment is shown in FIGS. 3A to3C. A sensing portion 7 of the sensor 100 is formed on a silicon oninsulator substrate (i.e., SOI substrate) 6 with using semiconductorprocessing techniques such as a micro-machining method. The SOIsubstrate 6 includes the first semiconductor layer 3, the secondsemiconductor layer 4, and an insulation layer 5. The first and secondsemiconductor layers 3, 4 are made of single crystal silicon. Theinsulation layer 5 as a sacrifice layer is made of, for example, oxidesilicon.

The sensing portion 7 includes a movable portion 8 and a pair of fixedportions 9, 10. Between the movable portion 8 and the fixed portion 9,10, a predetermined distance is set, so that they are insulated eachother. The movable portion 8 includes a pair of movable electrodes 1 a,1 b, a weight portion 11, a spring portion 12, an anchor 13, and anelectrode pad 14. The movable electrodes 1 a, 1 b are protruded fromboth sides of the weight portion 11 so as to be along with anacceleration direction Z shown in FIG. 3A. The movable electrodes 1 a, 1b are integrally formed with the weight portion 11. Each movableelectrode 1 a, 1 b has, for example, ten teeth disposed on each side ofthe weight portion 11. The weight portion 11 as a mass is applied withthe acceleration. The anchor 13 connects to the first semiconductorlayer 3 through the insulation layer 5. The spring portion 12 has abeam, both ends of which are fixed, so that the spring portion 12connects the weight portion 11 and the anchor 13. The spring portion 12is disposed perpendicularly to the acceleration direction Z. The springportion 12 has, for example, four beams.

In a region where the movable electrodes 1 a, 1 b, the weight portion11, and the spring portion 12 are formed, the first semiconductor layer3 and the insulation layer 5 are selectively etched and eliminated sothat the bottom of the second semiconductor layer 4 is exposed. Thespring portion 12 connecting to the weight portion 11 has a springfunction for moving along with the acceleration direction Z. Therefore,when the sensor 100 is applied with the acceleration including acomponent of the acceleration direction Z, the weight portion 11 and themovable electrodes 1 a, 1 b are displaced in the acceleration directionZ. After the acceleration disappears and no acceleration applies to thesensor, the spring portion 12 returns to a neutral position. Therefore,the weight portion 11 and the movable electrodes 1 a, 1 b also return tothe neutral position, respectively.

The movable portion 8 vibrates sympathetically, i.e., resonatesaccording to the vibration frequency of the acceleration. A resonantfrequency ωn of the movable portion 8, which is parallel to thesubstrate 6, is described as Formula F8. $\begin{matrix}{{\omega\quad n} = {\frac{1}{2\pi}\sqrt{\frac{16{YM}^{3}}{S\quad\rho\quad N^{3}}}}} & ({F8})\end{matrix}$

Here, Y represents the Young's modulus (i.e., Y is 170 GPa), M a widthof the spring portion 12, S an area of the weight portion 11, the areais parallel to the substrate 6, i.e., the area of the upper surface ofthe weight portion 11, ρ a mass density (i.e., ρ is 2330 kg/m³), and N alength of the spring portion 12. Accordingly, the movable portion 8 isformed so as to be satisfied with Formula F8 so that the resonantfrequency ωn of the movable portion 8 coincides with the vibrationfrequency of the acceleration. Thus, the displacement of the movableportion 8 can be amplified with using the resonant effect.

The electrode pad 14 is formed on the anchor 13, and connects to anouter electrical circuit such as capacitance-voltage (i.e., C-V) convertcircuit.

Each fixed portion 9, 10 includes a fixed electrode 2 a, 2 b, anelectrode pad 15 a, 15 b, and an anchor 16 a, 16 b, respectively. Theelectrode pad 15 a, 15 b is formed on the anchor 16 a, 16 b. The anchor16 a, 16 b is parallel to the weight portion 11. The fixed electrode 2a, 2 b is protruded from the anchor 16 a, 16 b, and faces the movableelectrode 1 a, 1 b protruded from the side of the weight portion 11. Thefixed electrode 16 a, 16 b is parallel to the movable electrode 1 a, 1b, so that a predetermined distance between the fixed electrode 2 a, 2 band the movable electrode 1 a, 1 b is provided. The anchor 16 a, 16 b isfixed on the first semiconductor layer 3 through the insulation layer 5.The bottom of the second semiconductor layer 4 composing the fixedelectrode 2 a, 2 b is exposed so that the fixed electrode 2 a, 2 b iscantilevered with the anchor 16 a, 16 b. In the first embodiment, eachfixed electrode 2 a, 2 b has ten teeth, which is the same number as theteeth of the movable electrode 1 a, 1 b. The movable electrode la andthe fixed electrode 2 a provide the first detection portion 17, and themovable electrode 1 b and the fixed electrode 2 b provide the seconddetection portion 18.

The electrode pads 15 a, 15 b are formed on the anchors 16 a, 16 b,respectively. The pads 15 a, 15 b are connected to the C-V convertcircuit. Although each of the movable electrodes 1 a, 1 b and the fixedelectrodes 2 a, 2 b has ten teeth, each of them can have other number ofteeth such as five or fifteen teeth.

In the sensor 100, the first detection portion 17 provided by themovable electrode 1 a and the fixed electrode 2 a has a totalcapacitance of CS1. The second detection portion 18 provided by themovable electrode 1 b and the fixed electrode 2 b has a totalcapacitance of CS2. In a case where no acceleration is applied to thesensor 100, the movable and fixed electrodes 1 a, 1 b, 2 a, 2 b arearranged in a predetermined position so that the difference δC betweenthe total capacitances CS1 and CS2 (i.e., C=CS1−CS2) becomes almostzero.

When the movable portion 8 is applied with the acceleration in theacceleration direction Z, the weight portion 11 moves in theacceleration direction Z. Together with the weight portion 11, themovable electrodes 1 a, 1 b are displaced. Here, each facing surface ofthe movable and fixed electrodes 1 a, 1 b, 2 a, 2 b has a concavity andconvexity portion 19, 20, respectively, as shown ion FIG. 3C. Eachconcavity and convexity portion 19, 20 is disposed perpendicularly tothe facing surface. A convexity 19 a disposed on the movable electrode 1a, 1 b faces a convexity 20 a disposed on the fixed electrode 2 a, 2 b.Accordingly, when the movable electrode 1 a, 1 b is displaced, thecapacitance between the convexities 19 a, 20 a of the movable and fixedelectrodes 1 a, 1 b, 2 a, 2 b changes. Therefore, the capacitance of thefirst detection portion 17 changes with the variation of ΔCS1, and thecapacitance of the second detection portion 18 changes with thevariation of ΔCS2. The sum of the absolute value of the variations|ΔCS1|+|ΔCS2| is measured as a voltage change by the C-V convertcircuit, so that the acceleration is detected.

The sensor 100 according to the first embodiment is formed as follows.FIGS. 4A to 4D explain a manufacturing process for forming the sensor100. Here, FIGS. 4D is a cross-sectional view showing the sensor 100taken along line IVD-IVD in FIG. 3A. As shown in FIG. 4A, the SOIsubstrate 6 includes the first semiconductor layer 3, the insulationlayer 5 made of oxide film, and the second semiconductor layer 4. Thefirst and second semiconductor layers 3, 4 are made of silicon. Atfirst, the first silicon oxide film 21 is formed on the SOI substrate 6.Then, a contact hole 22 is formed in the first silicon oxide film 21.The contact hole 22 is used for the electrode pad 15 b on the fixedportion 10. In the contact hole 22, an aluminum film is formed so as toform the electrode pad 15 b.

As shown in FIG. 4C, the second silicon oxide film 23 is formed on thesubstrate 6 with the electrode pad 15 b. The second silicon oxide film23 is etched so as to have a predetermined pattern. After that, thesecond semiconductor layer 4 is etched from the surface of the SOIsubstrate 6 to the insulation layer 5 with using the second siliconoxide film 23 as a mask. The third silicon oxide film 24 is also formedon the bottom of the substrate 6, and etched to have a predeterminedpattern. The third silicon oxide film 24 is used as a mask for etchingthe bottom side of the substrate 6. The first semiconductor layer 3 isanisotropicly etched with alkaline solution such as tetra methylammonium hydroxide (i.e., TMAH). Then, the insulation layer 5 is etchedwith hydrofluoric acid (i.e., HF) so that the insulation layer 5 isremoved. Further, the silicon oxide films 21, 23, 24 disposed on thesubstrate 6 are removed with HF. Thus, the sensor 100 is accomplished.

Referring to FIGS. 5A to 5C, functions and structure of the concavityand convexity portions 19, 20 disposed on the movable and fixedelectrodes 1 a, 1 b, 2 a, 2 b will be explained as follows. The movableelectrode 1 b and the fixed electrode 2 b include the concavity andconvexity portions 19, 20 disposed perpendicularly to the facingsurface, respectively. In the first embodiment, eight convexities areformed on each tooth of the electrodes 1 b, 2 b. When no acceleration isapplied to the sensor 100, the convexity 19 a of the movable electrode 1b faces the convexity 20 a of the fixed electrode 2 b, and the concavity19 b of the movable electrode 1 b faces the concavity 20 b of the fixedelectrode 2 b, as shown in FIG. 5A. Namely, the convexity 19 a of themovable electrode 1 b and the convexity 20 a of the fixed electrode 2 bprovide a capacitance. Accordingly, when the acceleration in theacceleration direction Z is applied to the sensor 100, the movableelectrode 1 b is displaced along with the facing surface, i.e., in theacceleration direction Z, so that the capacitance between theconvexities 19 a, 20 a changes. For example, assuming that thecapacitance change of a pair of the convexities 19 a, 20 a defines asΔCo, a total capacitance change ΔC shown in FIG. 5B is 8×ΔCo.

Accordingly, as the number of concavities and convexities 19 a, 19 b, 20a, 20 b included in one tooth of the concavity and convexity portions19, 20 becomes large, or the number of the teeth of the concavity andconvexity portions 19, 20 becomes large, the whole capacitance change inthe sensor 100 becomes larger by the whole number of concavities andconvexities 19 a, 19 b, 20 a, 20 b included in the sensor 100. Thus, thesensor sensitivity of the sensor 100 is improved. Here, the movableelectrode 1 a and the fixed electrode 2 a disposed on the firstdetection portion 17 also include the concavity and convexity portions19, 20, respectively. Although the number of convexity 19 a, 20 adisposed on one tooth of the electrode 1 a, 1 b, 2 a, 2 b is eight,other number of convexity 19 a, 20 a can be formed on one tooth of theelectrode 1 a, 1 b, 2 a, 2 b.

Next, the functions of the sensor 100 having the concavity and convexityportions 19, 20 will be described as follows. As shown in FIG. 5A, whenno acceleration is applied to the sensor 100, the convexity 19 a of themovable electrode 1 b completely faces the convexity 20 a of the fixedelectrode 2 b. In this case, the width of the convexity 19 a, 20 a isdefined as L1, which is the length of the convexity 19 a, 20 a in theacceleration direction Z. The width of the concavity 19 a, 20 a isdefined as L2, which is the length of the concavity 19 a, 20 a in theacceleration direction Z. The distance between the convexities 19 a, 20a facing each other is defined as D. The depth of the concavity 19 b, 20b is defined as G. The maximum displacement of the movable portion 8 isdefined as Xmax, which corresponds to the acceleration in theacceleration direction Z. It is preferable that the concavity andconvexity portions 19, 20 are formed to satisfy the following formulasF9-F11.L1≧L2  (F9)L2≧2×Xmax  (F10)G≧D  (F11)

When the concavity and convexity portions 19, 20 satisfy formula F9, andthe width L1 of the convexity 19 a, 20 a is supposed to be constant, thenumber of the convexity 19 a, 20 a disposed on one tooth of the movableand fixed electrodes 1 a, 1 b, 2 a, 2 b becomes larger. Namely, theinitial capacitance C0 between a pair of the convexities 19 a, 20 a canbe secured to have a certain value, and, moreover, the whole capacitancechange in the sensor 100 becomes larger.

When the concavity and convexity portions 19, 20 satisfy formula F10,even when the movable portion 8 is displaced by the maximum displacementXmax, the convexity 19 a of the movable portion 1 a, 1 b moves within amid point of the concavity 20 b, which is neighboring to the convexity20 a of the fixed electrode 2 a, 2 b facing the convexity 19 a in aninitial state. Here, the initial state of the sensor 100 means in a casewhere no acceleration is applied to the sensor 100. Accordingly, therelationship between the capacitance change and the displacement of themovable portion 8 monotonically increases or decreases.

When the concavity and convexity portions 19, 20 satisfy formula F11,the total of the distance D between the facing surfaces of the convexity19 a of the movable electrode 1 a, 1 b and the convexity 20 a of thefixed electrode 2 a, 2 b and the depth G of the concavity 19 b, 20 bbecomes twice larger than the distance D. The capacitance between theconvexity 19 aand the concavity 20 b or the convexity 20 a and theconcavity 19 b is provided in relation to almost the total distance ofthe distance D and the depth G. The capacitance between the convexity 19a and the convexity 20 a is provided in relation to the distance D.Therefore, the capacitance between the convexity 19 a, 20 a and theconcavity 19 b, 20 b is sufficiently smaller than the capacitancebetween the convexity 19 a and the convexity 20 a so that thecapacitance between the convexity 19 a, 20 a and the concavity 19 b, 20b can be negligible. Thus, the whole capacitance change becomes large,so that the sensor sensitivity is improved.

Next, as shown in FIG. 5B, it is assumed that part of the convexity 19 aof the movable electrode 1 a, 1 b faces the concavity 20 b of the fixedelectrode 2 a, 2 b when no acceleration is applied to a sensor 101. Whenthe acceleration is applied to the sensor 101, the movable electrode 1a, 1 b is displaced in the acceleration direction Z. In case of thesensor 100 shown in FIG. 5A, the capacitance is reduced even when themovable electrode 1 a, 1 b moves upward or downward of the accelerationdirection Z in FIG. 5A. That is because the facing surface of theconvexity 19 a, 20 a is reduced. However, in case of the sensor 101shown in FIG. 5B, the capacitance is reduced when the movable electrode1 a, 1 b moves upward of the acceleration direction Z in FIG. 5B. Thatis because the facing surface of the convexity 19 a, 20 a is reduced.When the movable electrode 1 a, 1 b moves downward of the accelerationdirection Z in FIG. 5B, the capacitance is increased. That is becausethe facing surface of the convexity 19 a, 20 a is increased.Accordingly, the sensor 101 shown in FIG. 5B can detect the direction ofthe acceleration by detecting the increase and decrease from the initialcapacitance.

Further, in case of the sensor 101 shown in FIG. 5B, preferably thewidth L of the facing surface of the convexity 19 a, 20 a in theacceleration direction Z is almost half of the width L1 of the convexity19 a, 20 a in the acceleration direction Z. In this case, even when themovable portion 8 moves upward or downward, the relationship between thecapacitance change and the displacement of the movable portion 8monotonically increases or decreases. Further, the increase and decreaseare symmetrically appeared on the basis of the initial state. Therefore,the sensor can detect the vibration, i.e., the acceleration easily.

Furthermore, it is preferred that the maximum displacement Xmax of themovable electrode 1 a, 1 b is equal to or less than a half of the widthof the convexity 19 a, 20 a. In this case, when the movable electrode 8is displaced downward with the maximum displacement Xmax, the facingsurface is increased so that the convexity 19 a of the movable electrode1 a, 1 b completely faces the convexity 20 a of the fixed electrode 2 a,2 b. Accordingly, the relationship between the capacitance change andthe displacement of the movable portion 8 monotonically increases ordecreases.

Next, as shown in FIG. 5C, it is assumed that the convexity 19 a of themovable electrode 1 a, 1 b does not face the convexity 20 a of the fixedelectrode 2 a, 2 b when no acceleration is applied to a sensor 102.Namely, the convexity 19 a of the movable electrode 1 a, 1 b faces theconcavity 20 b of the fixed electrode 2 a, 2 b. It is preferred that onesidewall of the convexity 19 a and one sidewall of the convexity 20 aare on the same line. In this case, the capacitance is increased whenthe movable electrode 1 a, 1 b moves downward of the accelerationdirection Z in FIG. 5C. That is because the facing surface of theconvexity 19 a, 20 a is increased. When the movable electrode 1 a, 1 bmoves upward of the acceleration direction Z in FIG. 5C, the capacitanceis slightly decreased. That is because the facing surface of theconvexity 19 a, 20 a is reduced. Accordingly, the sensor 102 shown inFIG. 5C can detect the direction of the acceleration by detecting theincrease and decrease from the initial capacitance.

Further, in case of the sensor 102 shown in FIG. 5C, preferably thesubtracted width L2−L1 that the width L1 of the convexity 19 a, 20 a inthe acceleration direction Z is subtracted from the width L2 of theconcavity 19 b, 20 b in the acceleration direction Z is equal to orlarger than twice of the maximum displacement Xmax of the movableportion 8. In this case, the relationship between the capacitance changeand the displacement of the movable portion 8 monotonically increases ordecreases. However, when the movable portion 8 moves upward of theacceleration direction Z in FIG. 5C by the maximum displacement Xmax,i.e., when the convexity 19 a of the movable electrode 1 a, 1 b movesaway from the convexity 20 a of the fixed electrode 2 a, 2 b, the midpoint of the convexity 19 a of the movable electrode 1 a, 1 b and themid point of the concavity 20 b of the fixed electrode 2 a, 2 b aredisposed almost on the same line. Accordingly, the capacitance betweenthe convexity 19 a of the movable electrode 1 a, 1 b and the convexity20 a of the fixed electrode 2 a, 2 b is slightly affected by theneighboring convexity 20 a, which is neighboring to the convexity 20 ainitially facing the convexity 19 a.

Therefore, it is more preferable that the total of the width L1 of theconvexity 19 a, 20 a and the maximum displacement Xmax of the movableportion 8 is equal to or less than a half of the width L2 of theconcavity 19 b, 20 b. In this case, even when the movable portion 8moves by the maximum displacement Xmax, the convexity 19 a of themovable electrode 1 a, 1 b moves within the mid point of the concavity20 b of the fixed electrode 2 a, 2 b. Accordingly, the relationshipbetween the capacitance change and the displacement of the movableportion 8 monotonically increases or decreases.

In the sensors 100-102 according to the first embodiment, the movableportion 8 is formed to resonate at the acceleration vibration frequency,and the movable portion 8 is displaced in the sliding direction, inwhich the movable portion 8 is affected with the slide damping effect.Accordingly, the magnification Q of resonance becomes larger, so thatthe displacement of the movable portion 8 becomes large. Thus, thecapacitance change is also increased, so that the sensor sensitivity isimproved. Specifically, the sensor sensitivity is much improved in acase where the vibration frequency of the acceleration coincides to theresonant frequency, i.e., the acceleration having a predeterminedfrequency (i.e., the resonant frequency) can be detected by the sensoreffectively.

Moreover, a plurality of concavity and convexity portions 18, 19disposed on each facing surface of the movable and fixed electrodes 1 a,1 b, 2 a, 2 b are provided, so that the capacitance change is enhancedby the number of a pair of the convexities 19 a, 20 a of the concavityand convexity portions 18, 19. Thus, the sensor sensitivity is improved.

Although the concavity and convexity portion 19, 20 has a rectangularshape, the concavity and convexity portion 19, 20 can have other shapesuch as orthogonal, semicircular, triangular shapes as long as themovable electrode 1 a, 1 b and the fixed electrode 2 a, 2 b are disposedat the regular intervals. Therefore, each one of the concavity 19 a, 20a and the convexity 19 b, 20 b may have a different shape. However, itis preferred that all of the concavity 19 a, 20 a and the convexity 19b, 20 b have the same shape formed at regular intervals, because it isrequired to enlarge the capacitance change and to manufacture the sensoreasily.

Further, the sensor includes the sensing portion 7 formed on the firstsemiconductor layer 3, the sensing portion 7 having a plurality ofmovable portion 8, each of which resonates at the different vibrationfrequency. In this case, when the acceleration detected by the sensor isdisposed in a predetermined range of the vibration frequency, i.e., whenthe acceleration has the different vibration frequency, the sensor candetect the acceleration in the predetermined range. That is because themovable portion 8 resonates at the different vibration frequency in thepredetermined range.

Second Embodiment

A capacitance type acceleration sensor according to a second embodimenthas the movable electrode 1 a, 1 b and fixed electrode 2 a, 2 b, asshown in FIGS. 6A to 6C. The movable electrode 1 a, 1 b moves in aperpendicular direction of the facing surface. In this case, the squeezedamping effect works between the facing surfaces of the movable andfixed electrodes 1 a, 1 b, 2 a, 2 b. However, in a conventional sensor,the length L of the facing surface of the movable and fixed electrodes 1a, 1 b, 2 a, 2 b is longer than the height H of the facing surface.Therefore, the conventional sensor cannot detect a fine accelerationbecause of the squeeze damping effect.

The inventors examine the relationship between shape of the facingsurface and squeeze damping coefficient E in case of a parallel platemodel. Here, the parallel plate model includes a single movableelectrode 1 a, 1 b and a single fixed electrode 2 a, 2 b, which faceeach other. The examination is performed with using the followingReynolds equation. $\begin{matrix}{E = {\frac{64\beta\quad{PoA}}{\pi^{6}\omega\quad D}{\sum\limits_{m,{n = {odd}}}\frac{m^{2} + {R^{2}n^{2}}}{({mn})^{2}\{ {( {m^{2} + {R^{2}n^{2}}} )^{2} + {\beta^{2}/\pi^{2}}} \}}}}} & ({F12})\end{matrix}$

Here, β, A, and R in Formula F12 are defined as follows. $\begin{matrix}{\beta = \frac{12\mu\quad{{eff} \cdot L^{2}}\omega}{{PoD}^{2}}} & ({F13}) \\{{\mu\quad{eff}} = \frac{\mu}{1 + {9.638( \frac{\lambda}{D} )^{1.159}}}} & ({F14})\end{matrix}$A=LH  (F5)R=L/H  (F16)

Here, Po represents atmospheric pressure (i.e., Po=1.013×10⁵ Pa), μ aviscosity of the air (i.e., μ=1.82×10⁻⁵ Pa·s), λ a mean free path of theair (i.e., λ=6.515×10⁻⁸ m) D the distance between the electrodes (i.e.,D=4 μm), L (μm) the length of the facing surface of the movableelectrode 1 a, 1 b and the fixed electrode 2 a, 2 b (i.e., the length ofthe facing surface in the protrusion direction of the movable electrode1 a, 1 b protruded from the weight portion 11), H (μm) the height of thefacing surface of the movable and fixed electrodes 1 a, 1 b, 2 a, 2 b,and ω the vibration frequency. The vibration frequency ω is, forexample, set to 2 kHz, which is the resonant frequency of the movableportion 8.

FIGS. 6A to 6C show typical parallel plate models having a pair of thefacing surfaces, the length of which is L (μm), and the height of whichis H (μm). FIG. 7 shows a relationship between the aspect ratio L/H ofthe facing surface and the damping coefficient E. FIG. 7 also shows therelationship between the aspect ratio L/H and the capacitance changeΔCo. Here, the area of the facing surface is constant.

As shown in FIG. 7, the damping coefficient E becomes the maximum valuewhen the length L is equal to the height H, i.e., the facing surface hasa square shape. When one of the length L or the height H becomes long,and the other becomes short, the damping coefficient E is reduced.Namely, assuming that the area of the facing surface is determined tohave a certain area, the squeeze damping effect is reduced as thesurrounding length of the facing surface becomes longer.

When the height H of the facing surface becomes larger, the capacitancechange ΔCo is increased. The movable electrode 1 a, 1 b protrudes fromthe sidewall of the weight portion 11, which is perpendicular to thesurface of the first semiconductor layer 3. The height of the movableelectrode 1 a, 1 b is almost equal to the height of the weight portion11 (i.e., the thickness of the sidewall of the weight portion 11).Accordingly, when the height H of the movable electrode 1 a, 1 b becomeslarger, i.e., the facing surface has a vertical rectangular shape, theheight of the weight portion 11 also becomes large. Therefore, theweight M of the weight portion 11 becomes larger according to the heightof the weight portion 11. Accordingly, as described in Formula F4, themagnification Q of resonance becomes large, so that the displacement Xof the movable portion 8 becomes larger. Thus, the capacitance changeΔCo is increased.

The sensing portion 7 of a sensor 103 according to the second embodimentis shown in FIG. 8. When the sensor 103 is applied with the accelerationin the acceleration direction Z, the movable portion 8 is displaced inthe acceleration direction Z, which is perpendicular to the facingsurface of the electrodes 1 a, 1 b, 2 a, 2 b. Each facing surface of themovable and fixed electrodes 1 a, 1 b, 2 a, 2 b has a verticalrectangular shape. Namely, the height of the facing surface is largerthan the length of the facing surface. Therefore, the squeeze dampingcoefficient E becomes small. Further, the height of the weight portion11 is almost equal to the height of the movable electrode 1 a, 1 b, sothat the mass of the weight portion 11 becomes large.

Accordingly, the magnification Q of resonance is increased, and thedisplacement of the movable portion 8 at the resonance point is alsoenhanced, so that the capacitance change ΔCo becomes large. Thus, thesensor sensitivity is improved so that the sensor 103 can detect a fineacceleration.

Third Embodiment

A capacitance type acceleration sensor 104 according to a thirdembodiment has facing surfaces of the movable and fixed electrodes 1 a,1 b, 2 a, 2 b, and a predetermined angle (i.e., a tilt angle) betweeneach facing surface and the acceleration direction Z is set between 0°and 90°, as shown in FIG. 9E and 9F. Here, in the sensor 100 shown inFIGS. 3A, 9C and 9D, the movable portion 8 is displaced along with thefacing surface, and in the sensor 103 shown in FIGS. 8, 9A and 9B, themovable portion 8 is displaced in the perpendicular directionperpendicular to the facing surface. Namely, the facing surface in thesensors 100, 103 is disposed perpendicular or parallel to theacceleration direction z.

FIGS. 9A to 9F show the capacitance change ΔCo in case of various sensor100, 103, 104. FIGS. 9A to 9E also show a capacitance area shown as C,1.15C, and the like disposed between a pair of movable and fixedelectrodes 1 a, 1 b, 2 a, 2 b. The capacitance area is a square portionformed of the length of the facing surface and the distance between themovable and fixed electrodes 1 a, 1 b, 2 a, 2 b. When no acceleration isapplied to the sensor 100, 103, 104, both the length and the distanceare set to L, and the capacitance is set to C, as shown in FIGS. 9A, 9Cand 9E. When the acceleration is applied to the sensor 100, 103, 104,the movable portion 8, i.e., the movable electrode 1 a, 1 b is displacedby 0.1 L in the acceleration direction, as shown in FIGS. 9B, 9D and 9F.

As shown in FIGS. 9A and 9B, in case of the sensor 103, the movableelectrode 1 a, 1 b is displaced toward the fixed electrode 2 a, 2 b by0.1 L, so that the distance between the movable and fixed electrodes 1a, 1 b, 2 a, 2 b changes from L to 0.9 L. Then, the capacitance alsochanges from C to 1.111C.

As shown in FIGS. 9C and 9D, in case of the sensor 100, the movableelectrode 1 a, 1 b is displaced along with the facing surface by 0.1L,so that the length of the facing surface changes from L to 1.1L. Then,the capacitance changes from C to 1.1C.

As shown in FIGS. 9E and 9F, in a case where the acceleration directionZ inclines at a 45 degree against the facing surface, the movableelectrode 1 a, 1 b is displaced in the acceleration direction Z by 0.1L,so that the distance between the electrodes 1 a, 1 b, 2 a, 2 b changesfrom L to 0.93L, and the length of the facing surface changes from L to1.07L. Accordingly, the capacitance changes from C to 1.15C.

Thus, the sensor 104 has the largest capacitance change ΔCo, i.e., 0.15Camong the sensors 100, 103, 104. Namely, it is preferred that the tiltangle between the facing surface of the movable and fixed electrodes 1a, 1 b, 2 a, 2 b and the acceleration direction Z is in a range between0° and 90° so that the sensor 104 has a large capacitance change ΔCo.

The sensing portion 7 of the sensor 104 according to the thirdembodiment is shown in FIG. 10.

Next, the relationship between the tilt angle θ between the facingsurface and the acceleration direction Z and the capacitance change ΔCois examined in detail. Specifically, as shown in FIGS. 11A to 11C, asensor 105 has the length of the facing surface of L and the distancebetween the electrodes of L, i.e., the sensor 105 has a squarecapacitance area. A sensor 106 has the length of ½L and the distance ofL, i.e., the sensor 106 has a horizontal rectangular capacitance area. Asensor 107 has the length of 2L and the distance of L, i.e., the sensor106 has a vertical rectangular capacitance area. The movable portion isdisplaced by 0.1L in the acceleration direction Z, which inclines at thetilt angle θ against the facing surface.

FIG. 12 shows the relationship between the tilt angle θ and thecapacitance change ΔCo in case of various sensors 105, 106, 107. In FIG.12, a line S1 shows the capacitance change ΔCo that is the largest valueamong the sensors 100, 103 in a case where the sensor 100, 103 has thesquare capacitance area of the length of L and the distance of L and thetilt angle θ is 0° (that is in case of the sensor 100) or 90° (that isin case of the sensor 103). A line S2 shows the capacitance change ΔCothat is the largest value among the sensors 100, 103 in a case where thesensor 100, 103 has the horizontal rectangular capacitance area of thelength of ½L and the distance of L and the tilt angle θ is 0° or 90°. Aline S3 shows the capacitance change ΔCo that is the largest value amongthe sensors 100, 103 in a case where the sensor 100, 103 has thevertical rectangular capacitance area of the length of 2L and thedistance of L and the tilt angle θ is 0° or 90°.

As shown in FIG. 12, all of the sensors 105-107 have a certain tiltangle θ, at which the capacitance change ΔCo of the sensor 105-107 islarger than that of the sensors 100, 103. Namely, there are some tiltangles θ, at which the capacitance change ΔCo of each sensor 105-107 islarger than the corresponding line S1-S3. In a case where thecapacitance area is the horizontal rectangular, the capacitance changeΔCo of the sensor 106 in a certain range of the tilt angle θ is largerthan that of the sensors 100, 103. In the certain range, thedisplacement of the movable electrode 1 a, 1 b in the sliding directionS becomes larger. In a case where the capacitance area is the verticalrectangular, the capacitance change ΔCo of the sensor 107 in a certainrange of the tilt angle θ is larger than that of the sensors 100, 103.In the certain range, the displacement in the sliding direction Sbecomes larger. In a case where the capacitance area is the square, thecapacitance change ΔCo of the sensor 105 in almost all range of the tiltangle θ is larger than that of the sensors 100, 103. Specifically, whenthe tilt angle θ is 45°, the capacitance change ΔCo of the sensor 105becomes the maximum value.

Thus, in the sensor 104-107 according to the third embodiment, thefacing surface of the movable and fixed electrodes 1 a, 1 b, 2 a, 2 binclines at the tilt angle θ against the acceleration direction Z, thetilt angle θ being in a range between 0° and 90°. When the accelerationis applied to the sensor 104-107, the distance between the electrodesbecomes short and the length of the facing surface becomes long, or thedistance becomes long and the length becomes short, so that thecapacitance change becomes larger. Therefore, the sensor sensitivity ofthe sensor 104-107 is improved.

Further, when the capacitance area is the square, in a wide range of thetilt angle θ, the capacitance change ΔCo of the sensor 104-107 can beincreased. Furthermore, when the tilt angle θ is 45°, the capacitancechange ΔCo becomes the maximum value, so that the sensor sensitivity ismuch improved.

In this embodiment, the concavity and convexity portion 19, 20 can beformed on the facing surface of the movable and fixed electrodes 1 a, 1b, 2 a, 2 b. In this case, the sensor sensitivity is much improved.Preferably, when no acceleration is applied to the sensor 104-107, partof the convexity 19 a of the movable electrode 1 a, 1 b faces theconvexity 20 a of the fixed electrode 2 a, 2 b. In this case, when theacceleration is applied so as to increase the area of the facingsurface, the capacitance C is increased. When the acceleration isapplied so as to decrease the area of the facing surface, thecapacitance C is decreased. Accordingly, the sensor 104-107 can detectthe direction of the acceleration by detecting the increase and decreasefrom the initial capacitance.

Moreover, it is preferred that each facing surface of the convexities 19a, 20 a inclines at the tilt angle θ against the acceleration directionZ, the tilt angle θ being in a range between 0° and 90°. In this case,the capacitance change ΔCo becomes larger. Further, the facing surfaceis almost the square, and the tilt angle θ is 45°, the capacitancechange ΔCo become much larger. Specifically, in a case where the sensorhas the concavity and convexity portion 19, 20, the total capacitancechange ΔC is increased by the number of the convexities 19 a, 20 a.

Although the sensor 104-107 according to the third embodiment is thecapacitance type acceleration sensor with using the resonance of themovable portion 8, the sensor 104-107 can be another type of dynamicalquantity sensor.

Such changes and modifications are to be understood as being within thescope of the present invention as defined by the appended claims.

1-17. (canceled)
 18. A capacitance type acceleration sensor comprising:a semiconductor substrate; a weight portion supported with the substratethrough a spring portion; a movable electrode integrated with the weightportion; and a fixed electrode cantilevered with the substrate, whereinthe movable electrode together with the weight portion is displacedtoward the fixed electrode in accordance with acceleration applied tothe weight portion, wherein the movable electrode includes a facingsurface facing a facing surface of the fixed electrode so as to providea capacitor having a capacitance, wherein the capacitance of thecapacitor changes in accordance with a displacement of the movableelectrode so that an outer circuit detects the acceleration as acapacitance change, and wherein each facing surface of the movable andfixed electrodes inclines at a predetermined angle with respect to adisplacement direction, the predetermined angle being in a range between0° and 90°.
 19. The sensor according to claim 18, wherein each of themovable and fixed electrodes has a plurality of teeth, wherein the teethof the movable and fixed electrodes are disposed alternately so thatsidewalls of the teeth provide the facing surfaces, and wherein themovable electrode has a predetermined shape in such a manner that themovable portion resonates at a vibration frequency of the accelerationfor increasing the capacitance change.
 20. The sensor according to claim19, wherein each facing surface of the movable and fixed electrodes hasa length along with the facing surface, and wherein the length of thefacing surface is equal to a distance between the movable and fixedelectrodes so that the capacitor has a square shape when no accelerationis applied.
 21. The sensor according to claim 20, wherein each facingsurface of the movable and fixed electrodes inclines at almost 45 degreewith respect to the displacement direction.
 22. The sensor according toclaim 18, wherein each facing surface of the movable and fixedelectrodes has a concavity and convexity portion for increasing thecapacitance change, wherein the concavity and convexity portion has aplurality of concavities and convexities, each of which is disposed at apredetermined intervals, and wherein each convexity of the movableelectrode faces the convexity of the fixed electrode, respectively, whenno acceleration is applied.
 23. The sensor according to claim 18,wherein each facing surface of the movable and fixed electrodes has aconcavity and convexity portion for increasing the capacitance change,wherein the concavity and convexity portion has a plurality ofconcavities and convexities, each of which is disposed at apredetermined intervals, and wherein part of the convexity of themovable electrode faces the convexity of the fixed electrode when noacceleration is applied.
 24. The sensor according to claim 22, whereineach convexity of the movable and fixed electrodes has a facing surface,a pair of which faces each other for proving a capacitor, wherein eachfacing surface of the convexity of the movable and fixed electrodes hasa length along with the facing surface, and wherein the length of thefacing surface of the convexity is equal to a distance between a pair ofthe convexities of the movable and fixed electrodes so that thecapacitor between a pair of the facing surfaces of the movable and fixedelectrodes has a square shape when no acceleration is applied.
 25. Thesensor according to claim 24, wherein each facing surface of theconvexities of the movable and fixed electrodes inclines at almost 45degrees with respect to the displacement direction of the movableportion.